   The concept of semihypergroups arises naturally in abstract harmonic analysis in terms of left/right coset spaces and orbit spaces of certain actions which appear frequently in different areas of research including Lie groups, coset theory, homogeneous spaces, dynamical systems, ordinary and partial differential equations and orthogonal polynomials, to name a few. These objects arising from locally compact groups, although retain some interesting structures from the parent category, fail to be a topological group, semigroup or even a hypergroup [1]}, [2]}. Hence these kinds of objects that frequently appear while studying the classical theory of topological groups, fall out of the parent category and can not quite be studied or analysed with the existing general theory for hypergroups and topological groups.
